Problem

Calculate the centroid of the region between the curves f(x) = x² + 2 and g(x) = 2x + 5 for x in the interval [–1, 3].

Solution

In 4.11 in the textbook we find formulas to calculate the x and y coordinates of the centroid of a region lying between 2 curves:

A is the area of the region, which itself is computed using an integral.

We will swap positions of f(x) and g(x) for all the integral calculations, since f is less than g on the interval [–1, 3].

Now compute the centroids.

So the centroid is (1, 5.4). Here is a graph showing the curves and the centroid.